The invention relates to a method of determining parameters of a unit cell of a crystal structure, in particular the dimensions and orientation of a unit cell, using diffraction, comprising the following steps: a. directing X- or neutron rays at a crystal rotating over a predetermined angle; b. detection of the radiation reflected by the crystal on a two-dimensional detection surface; c. determining the position where the reflected radiation falls on the detection surface.
Such a method is known from practice. In the known method the reflections of the beams directed at the crystal are detected on a position-sensitive detector, for example, a photo-sensitive plate, and on the basis of these positions which are processed further, the cell parameters of the crystal structure are determined in order to explain the respective reflection positions on the detection surface. According to the prior art the crystal is repeatedly rotated over an angle of, for example, 1 or 2xc2x0. As a result, the cell parameter of the crystal structure determined by this prior art technique is cursed with relatively large inaccuracies. The position of the reflections in the two directions of the detector surface is indeed determined accurately; however, the position of the crystal has an uncertainty amounting to several tenths of degrees. The unit cells composing the crystal structure will then exhibit deviations of several hundredth to one tenth degree or even more, with respect to the corners that are distinguishable in the unit cells. This accuracy can be improved by limiting the rotation of the crystal during measuring to approximately 0.1 or 0.2xc2x0, however, the number of measurements required then increases correspondingly.
It is the object of the invention to provide a method for determining the parameters of a unit cell of a crystal structure that can be performed quickly and requires little measuring time.
To this end the method of determining parameters of a unit cell of a crystal structure using diffraction according to the invention is characterized in that the steps a, b and c are repeated, wherein in step a the crystal always rotates over the same angle, that in the first performance of the steps a, b and c the relative movement of the crystal in relation to the detection surface is determined by only the rotation of the crystal, that in a repeat-performance of the steps a, b and c the relative movement of the crystal in relation to the detection surface is determined by a rotation of the crystal identical to that of the first performance of the steps a, b and c, and by a further relative movement of the crystal in relation to the detection surface coupled thereto, and that the combination of the positions determined in the repeat performance of steps c determines the angle position of the crystal in relation to a reference value in which reflection of the beams occurs.
The idea of the invention is based on the intelligence that when performing repeat-measurements, the position of the reflections on the detection surface in relation to the previous measurement can only be influenced by the additional relative movement of the crystal in relation to the detection surface. Because the relative movement of the crystal in relation to the detection surface is known and added to the rotation of the crystal which is also known, it is possible by means of generally known techniques to determine the position of the crystal whereby the reflections have occurred. This position of the crystal, together with the position of the reflections on the detection surface, provides sufficient information to derive more accurately than with the prior art, the unit cell parameters that determine the crystal structure. Further details about the determination of the crystal structure may be left aside, as the person skilled in the art will be quite familiar with these.
Various embodiments of the method according to the invention are conceivable. A first embodiment of the method according to the invention is characterized in that in the first performance of the steps a, b and c the crystal rotates over a first predetermined angle, and that in the repeat-performance of the steps a, b and c the crystal rotates over the first predetermined angle and the detection surface is moved.
It is desirable that in the repeat-performance of the steps a, b and c the crystal rotate over a first predetermined angle and the detection surface be rotated over a second predetermined angle. This may conveniently be performed in existing diffraction devices such as marketed, for example, by Nonius B. V. at Delft.
A second embodiment of the method according to the invention is characterized in that in the first performance of the steps a, b and c the crystal rotates over the first predetermined angle, and that in the repeat-performance of the steps a, b and c the crystal rotates over the first predetermined angle while in addition undergoing a movement superposed on this rotation.
It is desirable that the superposed movement of the crystal be a rotation in a plane cutting the rotation plane in which the first predetermined angle lies. This method may also be performed very suitably using existing diffraction devices as marketed by Nonius B. V. at Delft.
The method according to the invention further differs from the prior art in so far that during measurement the first predetermined rotation angle of the crystal is approximately 20xc2x0 or more. By performing the measurements with such a relatively large angular displacement it is possible to obtain all the necessary information for the determination of the parameter of a unit cell of the crystal structure, even of very small unit cells, with just two successive measurements. By suitably choosing the additional relative movement of the detection surface in relation to the crystal it is moreover possible to render the method according to the invention sufficiently accurate. If in order to obtain this additional relative movement the detection surface is, for instance, rotated, the second predetermined angle may be adjusted to approximately 10xc2x0. Such an angle displacement is also useful if the additional movement is carried out by the crystal.